1. Field of the Invention
This invention relates to a method and apparatus for measuring AC (alternating current) electric power, and more particularly, to a method and apparatus in which active power is determined as the scalar product of an AC voltage vector and an AC current vector while reactive power is determined as the absolute value of the vector product of the above-mentioned two vectors.
2. Description of the Prior Art
With the advance of control engineering, various techniques have been developed and used to measure voltage and current as digital quantities so as to determine power from such digital quantities. In an example of the prior art as shown in FIG. 4, voltage input 21 and current input 22 are converted in digital quantities by analog-digital converters 23 and 24, respectively. A multiplier 25 calculates the product of the voltage input and the current input in digital quantities, and harmonics components of the product are eliminated by a low-pass filter 28. Thus, electric power P is produced at an active power terminal 32. The reason for using the low-pass filter 28 is in that the product of the voltage and current includes a second harmonics component as shown in the second term on the right-hand side of the following equation. ##EQU1## Here, V: RMS (root means square) value of voltage
I: RMS value of current PA0 .omega.: angular velocity PA0 .theta.: phase difference PA0 t: time
The first term on the right-hand side of the equation (1) represents active power P, and the second term thereof represents ripples or harmonics.
To eliminate the second term harmonics of the right-hand side of the above equation without using the low-pass filter 28, it has been practiced to integrate the product of the equation (1) over a time span corresponding to integral multiple of the fundamental period T of the voltage or current. In this case, integration of the right-hand side second term of the equation (1) becomes zero.
The reactive power Q can be calculated as follows; namely, the digital values of the voltage and current are squared by multipliers 26, 27, respectively, and harmonics thereof are removed by low-pass filters 29, 30, respectively, and then calculation of the following equation is carried out by a calculating circuit 31. ##EQU2##
The value of the reactive power Q thus determined is delivered to a reactive power terminal 33.
To control and/or protect electric facilities, high-speed detection of electric power is necessary. However, with the method using the above low-pass filter 28 for elimination of harmonics, the speed of power measurement is limited by that of the low-pass filter 28, and as long as suppressing harmonics content below a certain level through harmonics elimination, the speed of power measurement cannot be made fast enough for certain applications. Theoretically, it is possible to raise the speed of power measurement by sacrificing the level of harmonics content, but sometimes presence of harmonics in excess of a certain level cannot be tolerated. Thus, there is a pressing need for the development of a method for high-speed power measurement or a power measuring method with a quick response.
With the conventional method using the integration of the equation (1) over an integral multiple of the fundamental period T, when the frequency fluctuates, it becomes necessary to modify the integrating time in response to the frequency fluctuation, i.e., fluctuation in the period. Thus, such power measuring apparatus must have a frequency measuring means which is not necessary for power measurement itself and adds unnecessary cost to the power measuring apparatus. Further, power measurement is effected only after the frequency measurement, so that power measurement is possible only once in two cycles. Thus, the method using such integration has a shortcoming in that its power measurement is slow.